question_answer

A ray of light is incident normally on one of the face of a prism of angle 30o and refractive index \[\sqrt{2}\].  The angle of deviation will be                                                                            [KCET 2001]

A)            26o                                            

B)            0 o

C)            23 o

D)            15 o

Correct Answer: D

Solution :

                   \[A={{30}^{o}},\mu =\sqrt{2}\]. As we know                    \[A={{r}_{1}}+{{r}_{2}}\]=\[0+{{r}_{2}}\Rightarrow A={{r}_{2}}\].                    Applying Snell?s law for the surface \[AC\]                    \[\frac{1}{\mu }\]= \[\frac{\sin {{r}_{2}}}{\sin e}=\frac{\sin A}{\sin e}\]                    \[\Rightarrow \]\[\frac{1}{\sqrt{2}}=\frac{\sin {{30}^{o}}}{\sin e}\Rightarrow e={{45}^{o}}\]            \[\delta =e-{{r}_{2}}={{45}^{o}}-{{30}^{o}}=15{}^\circ \]